Lesson 20

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 20.

Students may have many ideas for adding these numbers. In the synthesis, students discuss what they notice about the first two expressions. Students may notice that the expressions are equal and that one expression might help them with the other.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “What do you notice about the first two expressions?” (They are both 14. If 6 was broken into 2 and 4, it would be the same expression.)

The purpose of this activity is for students to discuss different ways to solve a three-addend story problem in which none of the addends can be combined to make 10 without being decomposed. Students solve the problem in a way that makes sense to them. Some students may build each number separately on the 10-frames and see both are filled. Some students may manipulate the numbers and think \(8 + 7 + 5 = 8 + 2 + 5 + 5\). Different methods for solving are highlighted in the synthesis. It is important that the teacher represents student thinking, so that these methods are visible to all.

When students make sense of the story problems and connect the quantities in the story to an equation, they reason abstractly and quantitatively (MP2).

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.

• Read the task statement.
• 4 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for students who:
  • place 8, 7, and 5 counters on the 10-frames and see that they are both full
  • count on
  • represent the problem as \(8 + 2 + 5 + 5\)
  • use a known sum like \(8 + 8\) and then add 4 more.

• Invite previously identified students to share.
• “What did they do to find the sum?”
• Record each method with an equation.

In this activity students solve three-addend story problems within 20. Students use methods and representations that make sense to them. When students connect the quantities in the story to an equation, they reason abstractly and quantitatively (MP2). They think strategically and may either choose to use a double 10-frame or decompose and compose the numbers in a way that helps them see the sum as 10 and some ones (MP1, MP5).

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “We are going to solve some problems using the different methods we’ve been working on.”

• Read the task statement.
• 6–8 minutes: independent work time
• 4 minutes: partner discussion

• Invite students to share their method for each problem. 
• Record each method with an equation.